ar X iv : m at h - ph / 0 30 40 13 v 1 1 0 A pr 2 00 3 Squeezed Statistical Mechanics

We present a formulation of Statistical Mechanics based on the concept of the dimensionless characteristic thermodynamic function, which has the form of a negative Massieu-Planck generalized potential. This function is equivalent to the free energy of the system in kT units. We construct classes of configurations in terms of the constraints of the system and, by applying the condition of minimum for the dimensionless characteristic thermodynamic function, we develop ensemble theory. All expressions derived are formally valid for any system, regardless of its constraints. We present first the results for Boltzmann-Gibbs equilibrium statistical mechanics. The formulation shows the connections between ensembles and also between thermodynamics and statistical mechanics without making explicit use of the concept of probability, which is introduced after developing ensemble theory. A general theory of fluctuations is then also introduced. The treatment followed serves as a starting point to generalize Boltzmann statistical mechanics and a scheme for this generalization is proposed. To achieve that, we define a convenient squeezing function which restricts among the attainable Boltzmann-Gibbs configurations. As an example, Tsallis non-extensive statistics is rebuilt into our formulation and new insights in this theory are provided.